A control device of a vehicle drive device including an engine, an electric motor, and an engine clutch selectively coupling the engine to a power transmission path from the electric motor to drive wheels has hitherto been known. For example, this corresponds to a control device of a vehicle drive device described in Patent Document 1. The control device of a vehicle drive device of Patent Document 1 provides engine start control of temporarily releasing the engine clutch after allowing the engine clutch to start slipping before complete engagement when the engine is started during motor running using only the power of the electric motor for running. Specifically, in the engine start control, first, the engine clutch is allowed to slip so as to increase the engine rotation speed and, when the engine rotation speed reaches a predetermined rotation speed determined as enabling the self-sustaining rotation of the engine, the engine clutch is released. The control device of a vehicle drive device further increases the engine rotation speed with the engine clutch released, starts an engagement operation of the engine clutch after the engine rotation speed becomes higher than the electric motor rotation speed, and completely engages the engine clutch when the engine rotation speed is synchronized with the electric motor speed.